To find the square root of 3250, we can proceed by breaking it down into its prime factors and simplifying it.

### Step-by-step Solution:

1. **Prime Factorization of 3250:**
   \[
   3250 = 2 \times 5^3 \times 13
   \]

2. **Simplifying the Square Root:**
   \[
   \sqrt{3250} = \sqrt{2 \times 5^3 \times 13}
   \]

   Since we have \(5^2 = 25\) inside the square root, we can take it out:

   \[
   \sqrt{3250} = 5 \times \sqrt{2 \times 5 \times 13}
   \]

   Simplifying further:

   \[
   \sqrt{3250} = 5 \times \sqrt{130}
   \]

3. **Calculating the Approximate Value:**

   We can use a calculator to find the approximate square root of 130:

   \[
   \sqrt{130} \approx 11.4
   \]

   Therefore,

   \[
   \sqrt{3250} \approx 5 \times 11.4 = 57
   \]

### Conclusion:
\[
\sqrt{3250} \approx 57
\]

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you simplify square roots involving prime factorization?
2. What are the properties of square roots for multiplication and division?
3. How do you approximate square roots without a calculator?
4. What is the square root of a non-perfect square?
5. How do you solve quadratic equations involving square roots?

### Tip:
To simplify square roots, look for perfect square factors that you can take out of the square root!

Discover how to find the square root of 3250 using prime factorization and simplification techniques. This detailed guide walks you through the process, including key concepts such as square roots, prime factorization, and the properties of square roots. Perfect for students in Grades 8-10.

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